The chocolate factory delivers boxes in containers that can fit either 8 large boxes or 10 small boxes. They sent 86 boxes in a day, using more large boxes than small ones, so the question is how many containers were needed.
To solve the problem, we need to figure out how many large boxes and small boxes were used. Let's assume that they used x containers with large boxes and y containers with small boxes. We know that each container can fit 8 large boxes, so the total number of large boxes used is 8x. Similarly, each container can fit 10 small boxes, so the total number of small boxes used is 10y.
We are given that they used more large boxes than small ones, so we can assume that there were more containers with large boxes than with small boxes. This means that x > y. We are also given that they sent 86 boxes in total, so we can write an equation based on this:
8x + 10y = 86
We need to find the values of x and y that satisfy this equation and the inequality x > y. We can start by trying different values of x and y that satisfy x > y and see if they also satisfy the equation. After some trial and error, we find that x = 5 and y = 4 satisfy the equation and the inequality. This means that they used 5 containers with 8 large boxes each (40 large boxes in total) and 4 containers with 10 small boxes each (40 small boxes in total) to send the 86 Valentine's chocolate boxes. Therefore, they used a total of 9 containers.